Related papers: Lipschitz-aware Linearity Grafting for Certified R…
Randomized smoothing is the state-of-the-art approach to construct image classifiers that are provably robust against additive adversarial perturbations of bounded magnitude. However, it is more complicated to construct reasonable…
This paper proposes a theoretical and computational framework for training and robustness verification of implicit neural networks based upon non-Euclidean contraction theory. The basic idea is to cast the robustness analysis of a neural…
Real-life applications of deep neural networks are hindered by their unsteady predictions when faced with noisy inputs and adversarial attacks. The certified radius in this context is a crucial indicator of the robustness of models. However…
We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for…
Training convolutional neural networks (CNNs) with a strict 1-Lipschitz constraint under the $l_{2}$ norm is useful for adversarial robustness, interpretable gradients and stable training. 1-Lipschitz CNNs are usually designed by enforcing…
Relying on the premise that the performance of a binary neural network can be largely restored with eliminated quantization error between full-precision weight vectors and their corresponding binary vectors, existing works of network…
Neural networks (NNs) have emerged as a state-of-the-art method for modeling nonlinear systems in model predictive control (MPC). However, the robustness of NNs, in terms of sensitivity to small input perturbations, remains a critical…
The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…
The Lipschitz constant plays a crucial role in certifying the robustness of neural networks to input perturbations. Since calculating the exact Lipschitz constant is NP-hard, efforts have been made to obtain tight upper bounds on the…
Certified robustness is a critical property for deploying neural networks (NN) in safety-critical applications. A principle approach to achieving such guarantees is to constrain the global Lipschitz constant of the network. However,…
Estimating the Lipschitz constant of deep neural networks is of growing interest as it is useful for informing on generalisability and adversarial robustness. Convolutional neural networks (CNNs) in particular, underpin much of the recent…
Sensitivity-based robustness certification has emerged as a practical approach for certifying neural network robustness, including in settings that require verifiable guarantees. A key advantage of these methods is that certification is…
Deep Neural Networks are vulnerable to small perturbations that can drastically alter their predictions for perceptually unchanged inputs. The literature on adversarially robust Deep Learning attempts to either enhance the robustness of…
In this work we propose a graph-based learning framework to train models with provable robustness to adversarial perturbations. In contrast to regularization-based approaches, we formulate the adversarially robust learning problem as one of…
Recent studies on the adversarial vulnerability of neural networks have shown that models trained with the objective of minimizing an upper bound on the worst-case loss over all possible adversarial perturbations improve robustness against…
Despite the large success of deep neural networks (DNN) in recent years, most neural networks still lack mathematical guarantees in terms of stability. For instance, DNNs are vulnerable to small or even imperceptible input perturbations, so…
Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz…
Deep learning has achieved remarkable success across a wide range of domains, significantly expanding the frontiers of what is achievable in artificial intelligence. Yet, despite these advances, critical challenges remain -- most notably,…
Neural networks are getting better accuracy with higher energy and computational cost. After quantization, the cost can be greatly saved, and the quantized models are more hardware friendly with acceptable accuracy loss. On the other hand,…
Training convolutional neural networks (CNNs) with a strict Lipschitz constraint under the $l_{2}$ norm is useful for provable adversarial robustness, interpretable gradients and stable training. While $1$-Lipschitz CNNs can be designed by…